Can you check my answer? the following table shows the number of total text messages sent on the first few days of july. if this rate continues, what is the rate of change in this situation? july 1 / 35 july 2 / 70 july 3 /105 35 per day -35 per day 70 per day 105 per day

The rate of change is another way of saying slope 
since the total text messages increase by 35 each day the slope (rate of change) should be 35

Way to prove it if slope isn't as obvious:

since you have the day and the total text messages you can use day as x and total text messages as y giving you the coordinates of: (1,35) (2,70) (3,105)

then you can use the slope formula to find the slope 
m= (y₂-y₁)/(x₂-x₁) and pick two coordinates to plug in

I choose coordinates (1,35) and (2,70) to plug into the equation
m=(70-35)/(2-1)
m=35/1
m=35
so the rate of change is 35